Hi, long time lurker, first time poster.
I agree with the poster above me who discounted the idea that magical fire is any different than normal fire. To add to what the person above me said, if you're going to use the fact that the scenery in CT never caught on fire as some sort of proof that magical fire is different than non-magical fire, then I can retort with the idea that maybe one of the water innate people put out the fires after battles before they could cause damage to the surrounding areas. Both are the results of flawed reasoning, and, quite frankly, add nothing to the discussion.
The idea that she was ready to fight because of her paranoid suspicions is also asinine. First, no matter how paranoid she was, she still had to sleep. If I remember correctly, the orphanage scene took place pretty late at night, suggesting it was at least at a time where the kids were asleep and she was probably too tired to fight at her best. Secondly, it was a surprise attack. Even if she was sure someone could be after her, there would be very little she could do. What, she'd patrol the orphanage every night, all night long? Unlikely. No matter what, she was vulnerable, particularly with all of the children in harm's way. The game makes this abundantly clear.
So, it comes down to her strength vs. his strength. I have no doubt that Lucca could've defeated Lynx if all things were equal. Things, however, were definitely not equal. Lucca was, despite her best efforts, caught by surprise. She also felt the need to ensure the orphans' safety to the best of her ability. Engaging in a full-out fight near the children, with gun and magic blazing would've been the last thing someone as intelligent as Lucca would've attempted. And that's what makes her disappearance (and, presumably, death) so tragic. She willingly, knowingly, sacrificed herself because of her own kindness. This is storytelling 101 and, again, the game makes this clear.